Machines such as machine tools or measuring machines, for example, are usually equipped with clamping devices, with whose aid a component can be clamped for processing or for a measuring operation. Generally, such clamping devices are situated at rotatable spindles and are able to be tightened or untightened mechanically or with the aid of a pressurized medium or with the aid of a vacuum. Conventionally, in this context, for example, a pressure line is routed in an axis of rotation of the rotatable part and the working medium is supplied or discharged for the clamping operation or the release operation in the process. In general, such clamping devices have been tried and tested. It may happen, however, that technical reasons make it impossible to place the line for the medium in the axis of rotation. Complicated constructions are then required for routing the medium from the stationary part to the rotating part and to the clamping devices. Also, there are application situations in which the retrofitting of a clamping device operated using a medium is desired.